Most experts agree that the biggest deterrent to smoking is raising the cost of cigarettes. As a result, whatever impact graphic warnings had after they were introduced in Canada in 2000 depends heavily on the cost of cigarettes in that period.

The new study, carried out by researchers from the University of Illinois at Chicago and the University of Waterloo in Canada, argues that the F.D.A. erred in calculating cigarette costs in Canada. Published this month, it says the F.D.A. used cigarette excise tax rates, which rose significantly during the decade, instead of the prices actually paid by consumers, which fell. According to the study, that caused the F.D.A. to overestimate the effect of prices and underestimate the effect of graphic warnings.

Citing several alleged flaws in the F.D.A.’s analysis, the study concluded that the reduction in smoking attributable to Canada’s warning labels was 33 times to 53 times larger than the F.D.A.’s estimate. Had the United States adopted such labels in 2012, it said, the number of adult smokers would have fallen by 5.3 million to 8.6 million.

The Campaign for Tobacco-Free Kids, an advocacy group that favors graphic warning labels, urged the F.D.A. to use the study and other scientific evidence to come back with a label proposal that would satisfy the courts. Stronger, graphic warnings could save lives.